# Algebra - math word problems

1. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
2. Combinations 6 6 purses 9 flaps 12 straps Every combination must include 1 purse, 1 flap and 1 strap. How many possible combinations?
3. Tangent 3 In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
4. Four poplars Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be?
5. Two cities The car goes from city A to city B at an average speed of 70 km/h, back at an average speed of 50 km/h. If it goes to B and back at an average speed of 60 km/h, the whole ride would take 8 minutes less. What is the distance between cities A and B?
6. Collection of stamps Jano, Rado, and Fero have created a collection of stamps in a ratio of 5: 6: 9. Two of them had 429 stamps together. How many stamps did their shared collection have?
7. AP RT triangle The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
8. Two cyclists 2 At the same time, two cyclists left the towns A and B at constant speeds. The first one going from town A to town B, and the second one from town B to town A. At one point of the trip they met. After they met, the first cyclist arrived at town B in 36min,. They brought in d two kilos and t three kilos of bread to the store. By the end of the day, 14 two-kg bread were sold. How many kilos of bread remained in the store by the next day?
10. Chocolate I have a box of chocolate - white, milk and dark. The ratio of white to milk with dark is 3: 4. The ratio of white and milk to dark is 17: 4. Calculate what is the ratio between white, milk, dark chocolate.
11. Cube The sum of all cube edges is 30cm. Find the surface area of the cube.
12. Ten boys Ten boys chose to go to the supermarket. Six boys bought gum and nine boys bought a lollipop. How many boys bought gum and a lollipop?
13. On line On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
14. The farmer The farmer had 140 sheep. For the next year, she decided to change the number of sheep in ratio 10: 7. How many sheep will he have then?
15. Two resistors Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of
16. Circle described The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
17. Exponential warm Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degre
18. Digit sum How many are three-digit numbers that have a digit sum of 6?
19. Sum of inner angles Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
20. Height as diameter of base The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.

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